Such a method for the precision working of the tooth flanks of particularly hardened gears, in which the tool is moved parallel to the workpiece gear axis and a radial feed occurs intermittently thereto, is known from the German Paper "Werkstatt und Betrieb" 118th year (1985), No. 8, Pages 505 to 509. The longitudinal feed, however, demands machining time and should therefore be avoided.
In another known method, the tool is exclusively fed radially, thus making possible a shorter machining time. In order to machine the workpiece tooth system over its entire width, the tool tooth system must closely conform to the workpiece tooth system, which causes certain problems during the tool manufacture.
The mentioned disadvantages can be reduced or avoided, if work is done according to the so called diagonal method. The tool is thereby moved relative to the workpiece in a direction which extends inclined with respect to the workpiece axis. Depending on the width of the tool and the angle with respect to the workpiece axis, which angle is chosen for the feed direction, a relatively short feed path may possibly already be sufficient in order to move the point of engagement and also the common normal from one face of the workpiece tooth system over the tooth width to the other face. It is therefore of particular importance to choose the width of the tool in dependency from the method parameters.
The basic purpose of the invention is therefore to further develop the known method so that it can be carried out with a feed path which is as short as possible.
A further basic purpose of the invention is to improve the described tool so that it permits a feed path which is as short as possible during use with the diagonal method.
The German Book "Hurth, Zahnradschaben", Pages 210/211 discloses geometrical relationships between tool width, workpiece gear width, crossed-axes angle and diagonal angle for the finishing of the tooth flanks of non-hardened gears, which finishing is carried out according to the diagonal method, which, however, cannot be applied to methods which work with abrasive tools. One can take from the German book that the finishing gear is narrower than the workpiece gear. From this results that the mesh between the tool and workpiece gear does not take place over the entire tooth width of the workpiece gear. If machining is thereby done with a diagonal feed, then the hard-material granules, in a tool with abrasive tooth flanks, have the tendency in the area of the tooth edges "to bury" themselves increasingly into the tooth flanks of the workpiece gear teeth. This results, in this area, in a nonclean tooth flank surface and a premature breakdown of the tool due to a breaking off of the hard-material granules.
The geometrical relationships which are discussed below permit among others in a surprising manner a checking of whether for example an existing tool is suited for a given machining case with the least possible feed path without the feed path (2.multidot.s) itself being included in this check. If the tool can be used, then the necessary feed path (2.multidot.s) can be determined in just as simple a manner from the formula ##EQU2## derived from the triangle calculation.
The dependency of the tool width from the method parameters has special significance. If a tool, for example an existing tool with a width which is larger than indicted is used, then the width is not fully utilized. If a larger tool would first have to be manufactured, unnecessary extra expenses for the tool would result. Whereas, if the width of the tool is smaller than has been disclosed below, then the tooth flanks of the workpiece gear are not machined over the entire width unless the feed path would be extended accordingly, which, however in particular is supposed to be avoided.
The inventive tool is suited for use in precision-working methods, which utilize a two-flank contact, as well as for those, which utilize a one-flank contact.